Fractal,Multifractal Properties And Laplace Eigenvalues Of Weighted Koch Network

In this paper, we study the fractal dimension, multifractal properties and Laplace eigenvalues of weighted Koch network introduced by Dai et al. and Koch network introduced by Zhang et al.. Based on Koch network, weighted Koch network introduces a weight coe?cient ω which is between 0 and 1. When the ωis 1, the weighted Koch network becomes the Koch network.First, by the numerical calculation, we obtained the dependence relationship of the fractal dimension on the weight parameter ω of the weighted Koch network.We found that the empirical fractal dimensions of the weighted Koch network coincide with the theoretical formula given by Dai et al. So the algorithm used in this thesis is suitable for the weighted Koch network. We also obtained the τ(q)curves of the average quality distribution and the curves of generalized fractal dimensions D(q) of the weighted Koch network. It was found that multifractality exists in these networks. The information dimension ?D(1)? and the correlation dimension ?D(2)? of the weighted Koch network are quadratic function of the parameter ω.Second, Koch network is a special case of the weighting Koch network. So our algorithm is also suitable for the Koch network. By the numerical calculation,we got the fractal dimension...